This question asks about how to intersect a ray with a bezier triangle: Intersect Ray (Line) vs Quadratic Bezier Triangle
What would happen if we had a bezier triangle that had scalars for control points, so they only controlled the height of each point on a triangle?
Would it be much easier then to find where a line intersected it?
Unfortunately I'm not sure where to even start, other than this equation, the explicit quadratic Bezier triangle! Anyone able to help me out?
$y = P_0S^2+2P_1ST+2P_2SU+P_3T^2+2P_4TU+P_5U^2$
$S,T,U$ are the barycentric coordinates of the triangle and $P_i$ are the scalar control points.
How would I go about finding where a line intersected with such an object, if it did at all?